1. Getting buggy articles' intro (image captions showing even if disabled.
2. When disabling photo gallery and related video, still showing in front-end.
Would be better if you could add a plugin or module to be able to display intro articles on joomla frontpage itself.
Waiting for a stable version .
Regarding the display of elements in the frontend, make sure you've set both the global parameters in K2 and the params of each menu item you create. It's essential to properly display things. ;)
The current module is pretty powerful to do what you ask already.